A SWAP gate for qudits

We present a quantum SWAP gate valid for quantum systems of an arbitrary dimension. The gate generalizes the CNOT implementation of the SWAP gate for qubits and keeps its most important properties, like symmetry and simplicity. We only use three copies of the same controlled qudit gate. This gate can be built with two standard higher-dimensional operations, the Quantum Fourier Transform and the d-dimensional version of the CZ gate

Simple quantum password checking

We present a quantum password checking protocol where secrecy is protected by the laws of quantum mechanics. The passwords are encoded in quantum systems that can be compared but have a dimension too small to allow reading the encoded bits. We study the protocol under different replay attacks and show it is robust even for poorly chosen passwords.Comment: 5 pages. Comments welcom

Multiple photon Hamiltonian in linear quantum optical networks

We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based on the effective Hamiltonian of the optical system for a single photon and comes from relating the evolution in the Lie group that describes the unitary evolution matrices in the Hilbert space of the photon states to the evolution in the Lie algebra of the Hamiltonians for one and multiple photons. We give a few examples of how a group theory approach can shed light on some properties of devices with two input ports.Comment: 6 pages. Comments welcom